Convergence to equilibrium for a second-order time semi-discretization ofthe Cahn-Hilliard equation

AIMS Mathematics

关键词: : ;    Łojasiewicz-Simon inequality;    gradient flow;    Cahn-Hilliard;    backward differentiation formula;   

DOI  :  10.3934/Math.2016.3.178

学科分类：数学（综合）

来源: AIMS Press

【 摘 要 】

We consider a second-order two-step time semi-discretization of the Cahn-Hilliard equation with an analytic nonlinearity. The time-step is chosen small enough so that the pseudo-energy associated withdiscretization is nonincreasing at every time iteration. We prove that the sequence generated by the scheme converges to a steady state as time tends to infinity. We also obtain convergence rates in the energy norm. The proof is based on the Łojasiewicz-Simon inequality.

【 授权许可】

CC BY